To see your site orders go to the menu Add-ons > Store > Orders
. Most of the order status' are set by default.
For example, when an order is paid on PayPal will have the status "Paid". Whereas a wire transfer will have the status "Awaiting verification" and as soon as you decide to verify the order the status is marked as "Paid". You can modify your delivery status after payment.
Each step of the process will be emailed to the client, at the moment you confirm the change.